Extracorporeal shock wave lithotripsy (ESWL) has been used routinely for the treatment of kidney stone patients for almost two decades. Despite the widespread clinical application, the underlying physical mechanisms of stone comminution and tissue injury in ESWL have not been fully understood yet. In fact, although some progress has been made recently on the development of better lithotripters and treatment protocols for stone fragmentation, these new machines have also resulted in an increase in both treatment imes and soft tissue injuries;leaving the original Dornier HM3 lithotripter as the gold standard for ESWL. A possible reason for this lack of improvement is that the great majority of ESWL studies have been focused primarily on experimental approaches while, in contrast, there has been a very limited development in realistic and accurate mathematical models that can capture the essential physics of shock wave propagation, focusing, cavitation, and their interactions with renal calculi and surrounding tissue. Our goal is to develop, and experimentally validate, such a comprehensive model where all the important mechanisms in ESWL will be accounted for and coupled together. The model will include effects deriving from pure shock propagation, absorption, streaming, cavitation and bubble dynamics, as well as those associated with the elastic stresses generated in the stone. It will also be fast and accurate in simulating realistic ESWL treatments without the need of supercomputers. The relevance of this research to public health is that, once developed, this model could significantly advance our basic knowledge of how ESWL works, it could provide considerable guidance for improving the treatments'efficacy and safety of existing systems, and it could aid in the design of the next generation lithotripters.